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Rational Polygons as Rotation Sets of Generic Homeomorphisms of the Two-Torus
Alejandro Passeggi
Mathematics , 2012, DOI: 10.1112/jlms/jdt040
Abstract: We prove the existence of an open and dense set D\subset? Homeo0(T2) (set of toral homeomorphisms homotopic to the identity) such that the rotation set of any element in D is a rational polygon. We also extend this result to the set of axiom A dif- feomorphisms in Homeo0(T2). Further we observe the existence of minimal sets whose rotation set is a non-trivial segment, for an open set in Homeo0(T2).
Examples of Minimal Diffeomorphisms on $t^{2}$ Semiconjugated to an Ergodic Translation
Alejandro Passeggi,Martin Sambarino
Mathematics , 2010,
Abstract: We prove that for every $\epsilon>0$ there exists a minimal diffeomorphism $f:\T^{2}\rightarrow\T^{2}$ of class $C^{3-\epsilon}$ and semiconjugate to an ergodic traslation, and have the following properties: zero entropy, sensitivity with respect to initial conditions and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Ma\~{n}\'e's example of derived from Anosov diffeomorphism on $\T^3.$
A classification of minimal sets for surface homeomorphisms
Alejandro Passeggi,Juliana Xavier
Mathematics , 2012,
Abstract: We classify minimal sets of (closed and oriented) hyperbolic surface homeomorphisms by studying the connected components of their complement. This extends the classification given by F. Kwakkel, T.J\"ager and A. Passeggi in the torus. The given classification is studied in the non-wandering setting and in light of the Nielsen-Thurston Theory.
A experiência em forma o =The experience in training
Passeggi, Maria da Concei??o
Educa??o , 2011,
Abstract: Focaliza-se as narrativas autobiográficas como prática pedagógica, com o objetivo de refletir sobre a ressignifica o da experiência, no contexto da forma o de formadores. Inicialmente, exp em-se alguns recortes históricos para definir a no o de experiência e pontuar aproxima es sobre sua fluidez e impermanência, a partir dos estudos de Dilthey, Gadamer, Jay e Ricoeur. Apresenta-se, em seguida, o grupo reflexivo como dispositivo de forma o de formadores e discutem-se as diferentes etapas do seu funcionamento nos ateliês de escrita autobiográfica, que constituem a parte prática de uma disciplina teórica sobre pesquisa (auto)biográfica, na pós-gradua o. Finalmente, traz-se nosso entendimento sobre os vínculos que se entretecem entre linguagem, reflexividade biográfica e consciência histórica, nas narrativas de si. Nas considera es em aberto, problematiza-se o lugar da escrita autobiográfica como prática de forma o na modernidade avan ada. We will lay our emphasis about autobiographical narratives as pedagogical practice in order to think on the redefinition of experience in the training of trainers context. We bring, first, some historical analysis to define the notion of experience and to punctuate approaches about its fluidity and impermanence, from studies of Dilthey, Gadamer, Jay and Ricoeur. Next, we will present the reflexive group, as a device to train trainers, and we will discuss the different stages of its operation in the studios of autobiographical writing, which is the practical part of a theoretical course on (auto) biographical research, in graduate school. Finally, we bring our understanding about the links that are interwoven between language, biographical reflexivity and historical awareness, in the narratives of one′s self. In the open considerations, we will discuss the place of autobiographical writing as practical training in advanced modernity.
On Torus Homeomorphisms Semiconjugate to irrational Rotations
Tobias J?ger,Alejandro Passeggi
Mathematics , 2013,
Abstract: In the context of the Franks-Misiurewicz Conjecture, we study homeomorphisms of the two-torus semiconjugate to an irrational rotation of the circle. As a special case, this conjecture asserts uniqueness of the rotation vector in this class of systems. We first characterise these maps by the existence of an invariant foliation by essential annular continua (essential subcontinua of the torus whose complement is an open annulus) which are permuted with irrational combinatorics. This result places the considered class close to skew products over irrational rotations. Generalising a well-known result of M. Herman on forced circle homeomorphisms, we provide a criterion, in terms of topological properties of the annular continua, for the uniqueness of the rotation vector. As a byproduct, we obtain a simple proof for the uniqueness of the rotation vector on decomposable invariant annular continua with empty interior. In addition, we collect a number of observations on the topology and rotation intervals of invariant annular continua with empty interior.
Rotation sets and almost periodic sequences
Tobias J?ger,Alejandro Passeggi,Sonja ?timac
Mathematics , 2014,
Abstract: We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segments as well as non-convex and even plane-separating continua. This shows that restrictions holding for rotation sets on the whole torus are not valid on minimal sets. The proof uses a construction of rotational horseshoes by Kwapisz to transfer the problem to a symbolic level, where the desired rotational behaviour is implemented by means of suitable irregular Toeplitz sequences.
Rotation intervals and entropy on attracting annular continua
Alejandro Passeggi,Rafael Potrie,Martín Sambarino
Mathematics , 2015,
Abstract: We show that if f is an annular homeomorphism admitting an attractor which is an irreducible annular continua with two different rotation numbers, then the entropy of f is positive. Further, the entropy is shown to be associated to a C^0-robust rotational horseshoe. On the other hand, we construct examples of annular homeomorphisms with such attractors so that the rotation interval is uniformly large but the entropy approaches zero as much as desired. The developed techniques allow us to obtain similar results dealing with Birkhoff attractors.
A Classification of Minimal Sets of Torus Homeomorphisms
Tobias Jaeger,Ferry Kwakkel,Alejandro Passeggi
Mathematics , 2011, DOI: 10.1007/s00209-012-1076-y
Abstract: We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.
Agronomic Use of Slurry from Anaerobic Digestion of Agroindustrial Residues: Effects on Crop and Soil  [PDF]
Amabelia del Pino, Omar Casanova, Mónica Barbazán, Victoria Mancassola, Laura Arló, Liliana Borzacconi, Mauricio Passeggi
Journal of Sustainable Bioenergy Systems (JSBS) , 2014, DOI: 10.4236/jsbs.2014.41009
Abstract:

In a greenhouse experiment we evaluated the application of slurry generated by a biogas reactor of agroindustrial residues. The objectives of this study were to determine the response to slurry application on dry matter production and nutrients absorption of Setaria italica (setaria), and to evaluate the effect of the slurry on soil properties. Two soils, of different texture, were mixed either with slurry or with diammonium phofsphate (DAP) at 0, 80, and160 kgN ha-1 equivalent rates. The setaria was harvested 68 days after planting, and separated into leaves plus stems, ears, and roots. Total biomass and content of N, P, K, Ca, Mg, Cu, Fe, Mn, and Zn were determined in each fraction. In the soil we determined pH, electric conductivity (EC), organic C, available P, mineral N, and exchangeable cations. Although the biomass produced and the amounts of nutrients absorbed were different in the two soils, in both of them setaria responded to the slurry application. The amounts of N absorbed from slurry and DAP were similar, indicating that the N from the slurry was readily available. The slurry application also increased the absorption of other macro and micro nutrients (P, Ca, Mg, and Zn). No significant changes in soil exchangeable cations, pH, and EC were observed at setaria harvest. In the silty soil the crop almost depleted the mineral N in all treatments, but in the sandy soil large amounts were left, especially in the treatments with slurry. This fact highlights the importance of a careful dosage of this soil amendment, to avoid the excess of mineral N, which is potential pollutant for the environment. It can be concluded that the use of slurry from the reactor had a positive effect on the nutrients availability, without negative effects on soil properties.

Análisis fitolíticos de suelos del sudoeste de la Provincia de Entre Ríos (Argentina) como una herramienta para comprender sus procesos pedológicos
Patterer, Noelia Isabel;Passeggi, Esteban;Zucol, Alejandro Fabián;
Revista mexicana de ciencias geológicas , 2011,
Abstract: in the present contribution, the presence and distribution of siliceous microremains in characteristic soil types of the southwestern entre ríos province (la curtiembre soil series) are analyzed. the phytolith extraction was made following a methodology that comprises the physical and chemical processing of the samples. the results show that the phytolith assemblages are dominated by graminoid phytoliths, associated with arecoid ones. the graminoid types are characterized by the presence of prismatic elongated, fan-shaped and polyhedrical phytoliths among the largest components. among the smallest phytoliths, bilobate and saddle types are abundant, especially in the samples from the upper and lower levels, whereas in the middle levels, roundel or truncated cones are more abundant. echinate globular phytoliths are present with scarce variations across the profiles. the abundance analysis allows interpreting the presence of three phytolith sources in soil profiles. the first one is the parental material, the tezanos pinto formation, principally abundant in the lower levels of the profiles. the second one originated in a past community that was present in early stages of the soils development, represented in the middle level samples of the profiles that clearly show evidence of material mobility along each profile. the third one is the phytolith assemblage of the upper levels, with a composition mainly linked to the current vegetation. the analyses demonstrated that these soils developed in a mixed community in association to a grassland dominated by panicoid and danthoniod affinities components, jointly with palms.
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